Thursday, June 04, 2009
Intro to Calculus (Class 88)
Lesson Title
Lesson for HW 30 (1): The Derivative Function from a Graphical Perspective
Geogebra Worksheet for the Lesson for Homework 30: The Derivative of a Function
”Derivative Matching Game”.
Overview
Today and Monday’s class are both focused on developing an understanding of the derivative function-- in other words, a function which represents the derivatives of another function for any value of x. In order to develop this concept students will begin from a graphical perspective aided by a dynamic worksheet.
Textbook Sections
§3.1 (Txt. p. 128) An Introduction to the Derivative: Tangents
Vocabulary
derivative function
differentiable
Key Attitudes
Math is about using what you know to create something new.
Key Ideas
For any differentiable function f(x), a slope (derivative) can be found for any value of x.
A function can be created using the derivatives (slopes) of another function.
A derivative function is positive on the intervals where the original function is increasing-- in other words, where the slope of the original function is positive.
A derivative function is negative on the intervals where the original function is decreasing-- in other words, where the slope of the original function is negative.
A derivative function is zero on the intervals where the original function is remaining constant-- in other words, where the slope of the original function is zero.
Key Skills
I can explain what is meant by “derivative function”.
I can determine over what interval a function is differentiable given the graph of the function.
When given four graphs, I can determine if any two represent a function and its derivative function.
I can sketch the graph of the derivative function when given the graph of a function.
I can sketch the graph of a function without using a calculator and then create a graph of the derivative function.
Turn-In (#87)
HW 29
Handouts
Lesson for Homework 30: The Derivative Function
Homework 30
Assignment
The Lesson for HW 30 and HW 30 are both due the day of the final
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.
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